13 citations · 24 across the 7 of their papers we have counts for
11 papers
On the Minkowski deficit for surfaces of revolution
Joaquim Bruna, Julià Cufí, Agustí Reventós
By studying the classical Minkowski's inequality, , relating area and mean curvature, in the particular case of convex surfaces of revolution, one is led to a functi…
A note on a result of Saks and Zygmund on additive functions of rectangles
Julià Cufí, Juan J. Donaire
We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.
Integral Geometry of pairs of planes
Julià Cufí, Eduardo Gallego, Agustí Reventós
We deal with integrals of invariant measures of pairs of planes in euclidean space as considered by Hug and Schneider. In this paper we express some of these integra…
The precise representative for the gradient of the Riesz potential of a finite measure
Julià Cufí, Augusto C. Ponce, Joan Verdera
Given a finite nonnegative Borel measure in , we identify the Lebesgue set of the vector-valued function $$V_{s}(x)…
Integral Geometry about the visual angle of a convex set
Julià Cufí, Eduardo Gallego, Agustí Reventós
In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. T…
A discrete approach to Wirtinger's inequality
Julià Cufí, Agustí Reventós, Carlos J. Rodríguez
Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classificati…
About the Jones-Wolff Theorem on the Hausdorff dimension of harmonic measure
Julià Cufí, Xavier Tolsa, Joan Verdera
These are the lecture notes of a seminar held at the Universitat Autònoma de Barcelona where the Jones-Wolff theorem about the dimension of harmonic measure in the plane is explain…
A note on Hurwitz's inequality
Julià Cufí, Eduardo Gallego, Agustí Reventós
Given a simple closed plane curve of length enclosing a compact convex set of area , Hurwitz found an upper bound for the isoperimetric deficit, namely $L^2-4πF\leq…
A lower bound for the isoperimetric deficit
Julià Cufí, Agustí Reventós
In this paper we provide a Bonnesen-style inequality which gives a lower bound for the isoperimetric deficit corresponding to a closed convex curve in terms of some geometrical inv…
Differentiability properties of Riesz potentials of finite measures and non-doubling Calderón-Zygmund theory
Julià Cufí, Joan Verdera
We study differentiability properties of Riesz potentials of finite Borel measures in dimension d larger than 2. The Riesz kernel has homogeneity 2-d. In dimension 2 we consider lo…
Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature
Julià Cufí, Agustí Reventós
We relate the total curvature and the isoperimetric deficit of a curve in a two-dimensional space of constant curvature with the area enclosed by the evolute of . We provide…